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A010101 Maximal size of binary code of length n and asymmetric distance 2. 4


%S 1,2,2,4,6,12,18,36,62

%N Maximal size of binary code of length n and asymmetric distance 2.

%C Size of optimal single-error-correcting code for Z-channel.

%C Next 3 terms are known to be in the range 112-117, 198-210 and 379-410 respectively.

%D S. Butenko, P. Pardalos, I. Sergienko, V. P. Shylo and P. Stetsyuk, Estimating the size of correcting codes using extremal graph problems, Optimization, 227-243, Springer Optim. Appl., 32, Springer, New York, 2009.

%D T. Etzion, New lower bounds for asymmetric and unidirectional codes, IEEE Trans. Inform. Theory, 37 (1991), 1696-1705.

%D J. H. Weber, Bounds and Constructions for Binary Block Codes Correcting Asymmetric or Unidirectional Errors, Ph. D. Thesis, Tech. Univ. Delft, 1989.

%D J. H. Weber, C. de Vroedt and D. E. Boekee, Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6, IEEE Trans. Inform. Theory, 34 (1988), 1321-1332.

%H Tuvi Etzion and Patric R. J. Östergård, <a href="https://doi.org/10.1109/18.651069">Greedy and heuristic algorithms for codes and colorings</a>, IEEE Transactions on Information Theory, 44 (1998), 382-388, [<a href="https://web.archive.org/web/20080612052947/http://www.tcs.hut.fi/~pat/codelist.html">Wayback Machine copy</a>].

%H N. J. A. Sloane, <a href="/A265032/a265032.html">Challenge Problems: Independent Sets in Graphs</a>

%K nonn,nice,hard

%O 1,2

%A _N. J. A. Sloane_

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)